{"paper":{"title":"On the complements of 3-dimensional convex polyhedra as polynomial images of ${\\mathbb R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.AG","authors_text":"Carlos Ueno, Jos\\'e F. Fernando","submitted_at":"2012-12-08T16:35:25Z","abstract_excerpt":"We prove that the complement ${\\mathcal S}:={\\mathbb R}^3\\setminus{\\mathcal K}$ of a 3-dimensional convex polyhedron ${\\mathcal K}\\subset{\\mathbb R}^3$ and its closure $\\overline{{\\mathcal S}}$ are polynomial images of ${\\mathbb R}^3$. The former techniques cannot be extended in general to represent such semialgebraic sets ${\\mathcal S}$ and $\\overline{{\\mathcal S}}$ as polynomial images of ${\\mathbb R}^n$ if $n\\geq4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1815","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}